A064320 - OEIS

%I #28 Mar 03 2020 01:30:52

%S 1,2,12,864,14929920,37150418534400000,

%T 10063619980174622195712000000000000000,

%U 664903611914043473202543232567979684173499596800000000000000000000000000000000000

%N a(n) = Product_{j=1..n} j^C(n-1,j-1).

%C Product variant of binomial transform of natural numbers.

%C From _Benoit Cloitre_, Jan 29 2002: (Start)

%C Array interpretation (first row and column are the natural numbers):

%C 1   2   3   4 .....

%C 2   2   6  12 ....

%C 3   4  12  72 ...

%C .......   864 ...

%C (End)

%F Main diagonal of array T(i, 1)=i, T(1, j)=j and T(i, j)=T(i-1, j)*T(i-1, j-1). - _Benoit Cloitre_, Aug 16 2003, corrected Apr 16 2015

%e a(5) = (1^1)*(2^4)*(3^6)*(4^4)*(5^1) = 1*16*729*256*5 = 14929920.

%p A064320:=n->product(i^binomial(n-1,i-1+0^(n-1)), i=1..n): seq(A064320(n), n=1..8); # _Wesley Ivan Hurt_, Apr 16 2015

%t Table[Product[j^Binomial[n - 1, j - 1], {j, 1, n}], {n, 8}] (* _Michael De Vlieger_, Apr 16 2015 *)

%o (PARI) a(n) = prod(j=1, n, j^binomial(n-1,j-1)); \\ _Michel Marcus_, Apr 17 2015

%Y Cf. A001792. Equals A064319(n, n).

%K nonn

%O 1,2

%A _Henry Bottomley_, Sep 10 2001